MCQ Questions for Class 12 Medical Physics Electromagnetic Induction Quiz 13

A coil having

$n$ turns and resistance

$4R$

$\Omega$ . This combination is moved in time

$t$ seconds from a magnetic field

$W_1$ weber to

$W_2$ weber. The induced current in the circuit is :

0%
$-\dfrac{W_2-W_1}{5Rnt}$
0%
$-\dfrac{(W_2-W_1)}{5Rnt}$
0%
$\dfrac{W_2-W_1}{Rnt}$
0%
$\dfrac{n(W_2-W_1)}{5Rt}$

A train is moving from south to north with a velocity of

$90$ km/h. The vertical component of earth's magnetic induction is

$0.4\times { 10 }^{ -4 }\quad Wb/{ m }^{ 2 }.$ If the distance between the two rails is

$1 m,$ what is the induced e.m.f. in its axle?

0%
$1mV$
0%
$0.1mV$
0%
$10mV$
0%
$100mV$

Explanation

By taraday's law,

Einduced -

$\frac{-d\phi }{dt}$

$\phi = \vec{B}.\vec{A} = |\vec{B}| |\vec{A}| cos\theta$

Here

$\theta = 0$ so,

$\phi = B.A$

$\dfrac{-d\phi }{dt} = \dfrac{dB.A}{dt} = \dfrac{-BdA}{dt}-\dfrac{AdB}{dt}$

As B is constant,

$\dfrac{dB}{dt} = 0$

$= \dfrac{d\phi }{dt} = \dfrac{-B.dA}{dt}$

Here,

$\dfrac{dA}{dt} = \dfrac{dlb}{dt} = \dfrac{ldb}{dt}+\dfrac{bdl}{dt}$

b(breadth) of the train is not

changing it a length that is going

into the field is varying with speed

90km/h(25m/s),so.

$\dfrac{dA}{dt} = l(0)+bv = (1)(25) = 25$

so,

$\dfrac{d\phi }{dt} = -(0.4) \times 10^{-4} \times 25 = 10^{-3}v$

Einduced =

$10^{-3}v = 1 mv$

Option - A is correct.

A rectangular loop of size

$(2m\times 1m$ ) is placed in x-y plane. A uniform but time varying magnetic field of strength

$\vec{B}=(20t\hat{i}+10t^{2}\hat{j}+50\hat{k})$ T where t is time elapsed in second. The magnitude of induced emf (in V) at time t is

0%
20+20 t
0%
20
0%
20 t
0%
zero

The mutual inductance between the rectangular loop and the long straight wire as shown in figure is M.

0%
$M = ZERO$
0%
$M=\frac { { \mu }_{ a } }{ 2\pi } ln(1+\frac { c }{ b } )$
0%
$M=\frac { { \mu }_{ 0 }b }{ 2\pi } ln(\frac { a+c }{ b } )$
0%
$M=\frac { { \mu }_{ 0 }a}{ 2\pi } ln(1+\frac { b }{ c } )$

A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizantal magnetic induction B as shown in the fig. At the position MNQ$$ the speed of the ring is v. then, the potential difference developed across the ring is

0%
$Zero$
0%
$1/2 BvR^2 M$ is at higher potential
0%
$\pi R Bv$ $Q$ s at higher potential
0%
$2R Bv$ and $Q$ is at higher potential

A wire of fixed length is wound on a solenoid of length l and radius r. Its self inductance is found to be L.Now if same wire is wound on a solenoid of length

$\dfrac{l}{1}$ and radius

$\dfrac{r}{2}$ , then self inductance will be

0%
2L
0%
$\dfrac{L}{2}$
0%
3L
0%
4L

A field strength of

$5 \times {10^4}/\pi$ ampere-turns / meter acts at right angle to a coil of

$50$ turns of area

${10^{ - 2}}{m^2}$ The coil is removed in

$0.1$ second

$.$ Then the induced emf in the coil is

$:$

0%
$0.1V$
0%
$80KV$
0%
$7.96V$
0%
none of the above

A conducting square loop of length

$1$ is placed in a magnetic field of Induction

$B _ { 0 }$ . End

$A$ and End

$C$ are moved away from each other so that the square loop becomes a straight line. If it's resistance is

$R$ then, the total charge flowing through the loop is:

0%
$\dfrac { B C ^ { 2 } } { \pi R }$
0%
< $\dfrac { B L ^ { 2 } } { R }$
0%
$\dfrac {B \cdot L ^ { 2 } } { R }$
0%
> $\dfrac { B _ { s } L } { R }$

A wire loop is placed in a region of time with varying magnetic field, which is oriented orthogonally to the plane of the loop, as shown in the figure. The graph shows the magnetic field variation as the function of time. Assume the positive emf is the one, which drives a current in the clockwise direction and seen by the observer in the direction of B. Which of the following graphs best represents the induced emf as a function of time ?

Two coils of self-inductances

$L_1 and L_2$ are placed so closed to each other that the effective flux in one coil is completely linked with the other, then the mutual inductance M between them is given by-

0%
$M=\sqrt { L_{ 1 }L_{ 2 } }$
0%
$M=L_{ 1 }-L_{ 2 }$
0%
$M=L_{ 1 }/L_{ 2 }$
0%
$M=L_{ 1 }+L_{ 2 }$

In a certain region static electric and magnetic fields exist. The magnetic field is given by

$\vec{B} = B_0 (\hat{i} + 2\hat{j} -4\hat{k})$ . If a test charge moving with a velocity

$\vec{v} = v_0 (3\hat{i} - \hat{j} + 2\hat{k})$ experiences no force in that region, then the electric field in the region, in SI units, is:

0%
$\vec{E} = -v_0B_0 (14\hat{j} + 7 \hat{k})$
0%
$\vec{E} = -v_0B_0 (\hat{i} + \hat{j} + 7 \hat{k})$
0%
$\vec{E} = v_0B_0 (3\hat{i} + 2\hat{j} - 4 \hat{k})$
0%
$\vec{E} = v_0B_0 (14\hat{j} + 7 \hat{k})$

Two coaxial coils are very close to each other and their mutual inductance is 5 mH.If a current l=10 sin 500 t is passed in one coil, then the peak value of induced emf in secondary coil is (where l is in A and t is in s)

0%
125 V
0%
25 V
0%
50 V
0%
100 V

A uniform but time varying magnetic field exists in cylindrical region and directed into the appear. If field decreases with time and a positive charge placed at any point inside the region, then if moves

0%
along 1
0%
along 2
0%
along 3
0%
along 4

A coil having n turns and resistance

$R\Omega$ , is connected in series with resistance

$R$ . This combination is moved in time t seconds from a magnetic field

$W_{1}$ weber to

$W_{2}$ weber. The induced current in the circuit is

0%
$- \frac{W_{2} - W_{1}}{5Rnt}$
0%
$- \frac{W_{2} - W_{1}}{5Rt}$
0%
$- \frac{W_{2} - W_{1}}{Rnt}$
0%
$- \frac{n(W_{2} - W_{1})}{5Rt}$

The magnetic induction at the centre

$O$ in the figure shown is

0%
$\dfrac {{\mu}_{0}i}{4}\left(\dfrac {1}{R_{1}}-\dfrac {1}{R_{2}}\right)$
0%
$\dfrac {\mu_{0}i}{4}\left(\dfrac {1}{R_{1}}+\dfrac {1}{R_{2}}\right)$
0%
$\dfrac {\mu_{0}i}{4}(R_{1}-R_{2})$
0%
$\dfrac {\mu_{0}i}{4}(R_{1}+R_{2})$

Explanation

Correct Answer: Option A

Hint: Resultant magnetic field is equal to sum of the magnetic field due to the currents in the two semicircles. This can be found using the equation of magnetic field at the centre of a loop.

Explanation of Correct Option:

Step 1: Finding magnetic field due to the two loops.

Let the magnetic field due to the semicircular loop of radius

$R_{1}$ be

$B_{1}$ and magnetic field due to the semicircular loop of radius $R_{2}$ be $B_{2}$

Resultant magnetic field at

$O=$ Magnetic field due to the semicircular loop of radius

$R_{1}$ + Magnetic field due to the semicircular loop of radius $R_{2}$

$=B_{1}+B_{2}$

Magnetic field at the centre of a current carrying loop $= \dfrac{\mu_{0}i}{2\ r}$

Magnetic field at the centre of a semicircular current carrying loop

$=\dfrac{1}{2}\times \dfrac{\mu_{0}i}{2\ r} = \dfrac{\mu_{0}i}{4\ r}$

$B_{1}=\dfrac{\mu_{0}i}{4\ R_{1}}$

$B_{2}=-\dfrac{\mu_{0}i}{4\ R_{2}}$ (Negative sign since the direction is opposite)

Step 2: FInding the magnetic field due to horizontal parts

We know,

$dB=\dfrac{\mu i}{4\pi}(\dfrac{\vec{dl}\hat{r}sin\theta} {r^{2}})$

Here since the angle is

$0^{\circ}$ and

$180^{\circ}$ , magnetic field due to the horizontal parts is zero.

Step 3: Finding magnetic induction at the centre.

Magnetic induction at the centre

$O, B= B_{1}+B_{2}$

$B=\dfrac{\mu_{0}i}{4\ R_{1}}+-\dfrac{\mu_{0}i}{4\ R_{2}}$

$B=\dfrac{\mu_{0}i}{4}(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$

The magnetic induction at centre in the shown figure is $B=\dfrac{\mu_{0}i}{4}(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}).$

2149150_1269655_ans_16c02897839241d19e78227dd2402b07.png

A charge of

${10^{ - 6}}C$ is describing a circular path of radius

$1$ cm making

$5$ revolution per second . The magnetic induction field at the centre of the circle is

0%
$\pi \times {10^{ - 10}}T$
0%
$\pi \times {10^{ - 9}}T$
0%
$\frac{\pi }{2} \times {10^{ - 10}}T$
0%
$\frac{\pi }{2} \times {10^{ - 9}}T$

A circular loop of radius A is placed in the same plane as a long straight wire carrying a current I. The centre of the loop is at a distance r from the wire where r>>a . The loop is moved away from the wire with a constant velocity v. The induced emf in the loop is

0%
$\xi =\mu_0 I/ 2\pi$
0%
$\xi =\mu _0I{a}^{2}/2 \pi {r}^{2}$
0%
$\xi =\mu _0I{a}^{2}V/2 \pi {r}^{2}$
0%
none of these

A closely wound coil of 100 turns and area of cross section

$1{cm}^{2}$ has a self-inductance 1 mH. The magnetic induction at the centre of the coil, when a current 2A flows in it, will be :

0%
$0.02 Wb/{{m}^{2}}$
0%
$0.4Wb/{{m}^{2}}$
0%
$0.8Wb/{{m}^{2}}$
0%
$1Wb/{{m}^{2}}$

A conducting circular ring and a conducting elliptical ring both are moving pure transnationally in a uniform magnetic field of strength

$B$ as shown in figure on a horizontal conducting pane potential difference between top most point of circle and ellipse is:

0%
$12va$
0%
$4vBa$
0%
$8vBa$
0%
$2vBa$

A long metal rod moves at a constant velocity in the direction perpendiular to the length and at constant magnetic field. choose the correct statement

0%
the entire rod is at the same electric potential
0%
there is electric field in the rod
0%
the electric potential is highest at the centre
0%
the electric potential is lowest at the centre

A coil having

$100$ turns and area of

$0.001 \, m^2$ is free to rotate about its diametric axis; the coil is placed with its plane perpendicular to magnetic field of

$1.0 \, \dfrac{Wb}{m^2}$ . If the coil is rotated rapidly through an angle of

$180^0$ , how much charge will flow through the coil ? The resistance of the coil is

$10 \,\Omega$

0%
$0.02$ coulomb
0%
$0.04$ coulomb
0%
$0.08$ coulomb
0%
$0.07$ coulomb

$1.2m$ wide track is parallel to the magnetic meridian. The verticle component of the earth's magnetic field is

$0.5$ gauss. When a train runs on the rails at a speed of

$60Km/hr$ , then the induced potential difference between the ends of its axle will be __

0%
$10^{-4} V$
0%
$2 \times 10^{-4} V$
0%
$10^{-3} V$
0%
Zero

Two cells of emf

$2V$ and

$1.5 V$ with internal resistance

$1 {\Omega}$ each are connected in parallel similar poles joined together. The combination is connected to an external resistance of

$10{\Omega}$ . Find the current through the external resistance.

0%
$5.96 \times 10^5 \, J \, kg^{-1}$
0%
$4.83 \times 10^5 \, J \, kg^{-1}$
0%
$3.34 \times 10^5 \, J \, kg^{-1}$
0%
$4 \times 10^5 \, J \, kg^{-1}$

Two coils A and B have mutual inductance

$2\times { 10 }^{ -2 }$ henry. If the current in the primary is

$i=5\sin { \left( 10\pi t \right) }$ then the maximum value of e.m.f.induced in coil B is

0%
$\pi \quad volt$
0%
$\pi /2volt$
0%
$\pi /3volt$
0%
$\pi /4volt$

An electron moves on a staight line path

$XY$ as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any,induced in the coil?

0%
No current induced
0%
abcd
0%
adcb
0%
The current will reverse its direction as the electron goes past the coil

A conducting rod moves with constant velocity u perpendicular to the long, straight wire carrying a current I as shown compute that the emf generated between the ends of the rod

0%
$\dfrac{{{\mu _0}\nu {\rm I}l}}{{\pi r}}$
0%
$\dfrac{{{\mu _0}\nu {\rm I}l}}{{2\pi r}}$
0%
$\dfrac{{2{\mu _0}\nu {\rm I}l}}{{\pi r}}$
0%
$\dfrac{{{\mu _0}\nu {\rm I}l}}{{4\pi r}}$

Explanation

The magnetic field near the conducting rod due to long current carrying wire is

$B=\dfrac{\mu_0I}{2\pi r}$ (using Ampere's law,

$\int B.dl=\mu_0I$ )

Now , induced emf due to moving rod is

$e=Blv=\dfrac{\mu_0I}{2\pi r}\times lv=\dfrac{\mu_0vIl}{2\pi r}$

A semicircular conducting ring is placed in

$yz$ plane in a uniform magnetic field directed along positive

$z$ -direction. An induced

$emf$ will be developed in the ring if it is moved along

0%
positive $x$ -direction
0%
positive $y$ -direction
0%
positive $z$ -direction
0%
$None\ of\ the\ above$

A wire in the form of a square of side a caries a current i. Then the magnetic induction at the centre of the square wire is( Magnetic permeability of free space=

${ \mu }_{ \circ }$ )

0%
None of these
0%
$\cfrac { \mu _ { 0 } i \sqrt { 2 } } { 2 \pi a }$
0%
$\cfrac { 2 \sqrt { 2 } \mu _ { 0 } t } { \pi a }$
0%
$\cfrac { \mu _ { 0 } t } { \sqrt { 2 } \pi \mathrm { a } }$

A wire carrying current

$I$ is tied between points

$P$ and

$Q$ and is in the shape of a circular arch of radius

$R$ due to a uniform magnetic field

$B$ (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle

$2 \theta _o$ at the centre of the circle (of which it form an arch) then the tension in the wire is :

0%
$\frac{{IBR{\theta _0}}}{{\sin {\theta _0}}}$
0%
$\frac{{IBR}}{{\sin {\theta _0}}}$
0%
$\frac{{IBR}}{{2\sin {\theta _0}}}$
0%
$IBR$

Two coils A and B have mutual inductance

$2\times { 10 }^{ -2 }$ henry. If the current in the primary is

$i=5\sin { \left( 10\pi t \right) }$ then the maximum value of e.m.f. induced in coil B is

0%
$\pi \quad volt$
0%
$\pi /2volt$
0%
$\pi /3volt$
0%
$\pi /4volt$

In the circuit shown, the power factor of the circuit is

$\dfrac { 3 }{ 5 }$ , Power factor of only RC circuit is

$\dfrac { 4 }{ 5 }$ , source voltage is

$100$ volt and its angular frequency

$\omega =100 rad/ sec$ . RMS current in circuit is A> If inductive reactance is greater then capacitive reactance then the value of self inductance L is

0%
$\dfrac { 1 }{ 2 } H$
0%
$\dfrac { 1 }{ 3 } H$
0%
$1 H$
0%
$\dfrac { 1 }{ 4 } H$

A rectangular, a square, a circular and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity

$\bar{V}=v\hat{i}$ . The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for

0%
The rectangular, circular and elliptical loops
0%
The circular and the elliptical loops
0%
Only the elliptical loop
0%
Any of the four loops

A current carrying wire (current

$= i$ ) perpendicular to the plane of the paper produces a magnetic field, as shown in the figure. A square of side

$a$ is drawn with one of its vertices on the centre of the wire. The integral

$\int \vec { B } d \vec { r }$ along

$OPQRO$ has the value

0%
$+ \mu _ { 0 } i$
0%
$\dfrac { \mu _ { 0 } i} { 8 }$
0%
$\dfrac { \mu _ { 0 } i} { 4 }$
0%
$\dfrac { \mu _ { 0 } i} { 2 }$

A straight wire of length L is bent a semicircle. It is moved in a uniform magnetic field with speed V with diameter perpendicular to the field. The induce emf between the ends of the wire is

0%
$BLv$
0%
$2BLv$
0%
$2 \pi BLv$
0%
$\cfrac {2BvL} \pi$

Explanation

Correct Answer: Option D
Step 1: Induced E.M.F across the diameter
We know, the E.M.F generated across the ends of a wire is

$\epsilon = vBl$ ....... to be remembered .....

$(I)$
Also we take the distance between the two points as the length (projected length).
So,

$l = 2R$

Step 2: Relate the length of wire and radius
The wire of length

$L$ is bent into a semicircle

$\therefore L = \pi R$

$R = \dfrac{L}{\pi}$

put in

$(I)$

$\epsilon = vB\times 2\times \dfrac{L}{\pi}$
or,

$\epsilon = \dfrac{2vBL}{\pi}$

Hence, correct answer is option D.

Mutual induction of the system of two coils do not depends upon

0%
number of turns of the coils.
0%
current in the coils.
0%
relative inclination of the coil.
0%
distance between two coil.

The figure shows a circular area of radius

$R$ where a uniform magnetic field

$\vec B$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field

$E(r)$ ?

Two coils are made of copper wires of the same length In the first coil the number of turns is 3

$\mathrm { n }$ and radius is

$r .$ In the second coil number of turns is

$\mathrm { n }$ and radius is 3

$\mathrm { r }$ the ratio of self-inductances of the coils will be:-

0%
$9 : 1$
0%
$3 : 1$
0%
$1 : 3$
0%
$1 : 9$

A conducting circular loop made of a thin wire, has area

$3.5\times 10^{ -3 }m^{ 2 }$ and resistance 10

$\Omega$ . It is placed perpendicular to a time dependent magnetic field B(t)=(0.4T)sin(50

$\pi$ t). The field is uniform in space. Then the net charge flowing through the loop during t=0 s and t=10 ms is close to :

0%
0.07 mC
0%
0.21 mC
0%
0.14 mC
0%
0.06 mC

A conducting disc of radius R rotates about its axis with an angular velocity

$\omega$ . Then the potential difference between the centre of the disc and its edge is ( no magnetic field is present)

0%
Zero
0%
$\frac{m_e\omega^2R^2}{2e}$
0%
$\frac{m_e\omega R^3}{3e}$
0%
$\frac{em_e\omega R^2}{3}$

In an A.C. sub-circuit as shown in figure, the resistance

$R = 0.2 \Omega$ . At a certain instant

$V_A -V_B = 0.5 V$ ,

$l =0.5 A$ , and current is increasing at the rate of

$\frac{\triangle l}{\triangle t} = 8 A/s$ . The inductance of the coil is

0%
0.01 H
0%
0.02 H
0%
0.05 H
0%
0.5 H

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

0%
decreases by a factor of 9
0%
increases by a factor of 27
0%
decreases by a factor of $9\sqrt { 3 }$
0%
Increases by a factor of 3

A coil is wound on a hollow insulating cylinder, which contains in it a laminated iron core. The dependence of inductance L with the displacement X of the iron core is shown in the figure. In the initial state X= 0 (the core is fully inserted into the coil), the current in the coil is 1.0 A. Find current in the coil immediately after the core is quickly taken out of the coil

0%
The current in the coil immediately after the core is quickly taken out of the coil is 5 amp.
0%
The current in the coil immediately after the core is quickly taken out of the coil is 2.5 amp.
0%
Magnetic flux associated with coil initially is 5 milli Tesla $m^2$
0%
Magnetic flux associated with coil just after quick removal is 5 mili Tesla $m^2$

An electron and a proton both having the same kinetic energy enters region of uniform magnetic field. In a plane perpendicular to the field.If their masses are denoted by in ans respectively then the ration the radii (electron to produced) of their circular orbits is

0%
$\sqrt { \frac { m\_ p }{ m\_ e } }$
0%
$$ \sqrt { \frac { m\_ e }{ m\_ p } }
0%
$\frac {m_e}{m_p}$
0%
1

In the following figure, the magnet is moved the coil with speed

$v$ and induced emf is

$e$ . If magnet and coil recede away from one another each moving with speed

$v$ , the induced emf in the coil will be

0%
$e$
0%
$2\ e$
0%
$\dfrac{e}{2}$
0%
$4\ e$

An average induced emf of 0.4 V appears in a coil when the current in it is changed from 10 A in one direction to 10 A in opposite direction in 0.5 sec. self-inductance of the coil is.

0%
50 H
0%
75 H
0%
0.008H
0%
100 H

The magnetic field in a certain cylindrical region is changing with time according to the law B=

$B=[16-4t^{2}]$ Tesla.. The induced electric field at point P at time t=2 sec.

0%
8 volt/m
0%
6 volt/m
0%
4 volt/m
0%
none

A conducting rod of length vector

$\vec{L}=(\frac{3}{5}\hat{j}+\frac{4}{5}\hat{k})$ ms moving with a velocity

$\vec{v}=2 \hat{i}$ m/sec in a uniform magnetic field

$\vec{B}=(\hat{j} - 2\hat{k})$ Tesla. Then the magnitude of induced emf in volt in the rod will be

0%
$2$
0%
$4$
0%
$6$
0%
$8$

The coefficient of self induction of two inductor coils are 20 mH and 40 mH respectively. If the cols are connected in series so as to support each other and the resultant inductance is 80 mH then the value of mutual inductance between the coils will be

0%
5 mH
0%
10 mH
0%
20 mH
0%
40 mH

Length of one metal rod is

$1$ meter.

$2T$ is the intensity of the magnetic field. When this rod is rotating with the frequency of

$10 Hz$ perpendicular to the field line by keeping its one end fixed as centre, induced emf is

0%
$10\pi$
0%
$20\pi$
0%
$30\pi$
0%
$40\pi$

A thin non-conducting ring of mass m carrying a charge q can freely rotate about its axis .Initially the ring is at rest and no magnetic field was present. When a uniform magnetic field is switched on, perpendicular to the plane of the ring, and increased with time according to the relation dB/dt=k the angular velocity of the ring as a function of is

0%
$\dfrac { kqt }{ 2m }$
0%
$\dfrac { kmt }{ 2q }$
0%
$\dfrac { 2mt }{ kq }$
0%
$\dfrac { 2kt }{ qm }$

CBSE Questions for Class 12 Medical Physics Electromagnetic Induction Quiz 13 - MCQExams.com

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Practice Class 12 Medical Physics Quiz Questions and Answers

CBSE Questions for Class 12 Medical Physics Electromagnetic Induction Quiz 13 - MCQExams.com

0:0:1

Practice Class 12 Medical Physics Quiz Questions and Answers

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